The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Given,

⇒ Diameter of the moon (d) = $\dfrac{1}{4}$ × diameter of the earth (D)

⇒ $\dfrac{d}{2} = \dfrac{1}{4} \times D$

⇒ Radius of the moon (r) = $\dfrac{1}{4}$ × radius of the earth (R)

⇒ r = $\dfrac{1}{4}$ × R

⇒ $\dfrac{r}{R} = \dfrac{1}{4}$ …….(1)

Now,

Surface area of earth = 4πR²

Surface area of moon = 4πr²

The ratio of their surface areas = $\dfrac{\text{Surface area of moon}}{\text{Surface area of earth}}$

$= \dfrac{4πr^2}{4πR^2} \\[1em] = \dfrac{r^2}{R^2} \\[1em] = \Big(\dfrac{r}{R}\Big)^2 \\[1em] = \Big(\dfrac{1}{4}\Big)^2 \\[1em] = \dfrac{1}{16}.$

Hence, the ratio of their surface area = 1 : 16.